The short version is you need not the "biggest aperture possible" but the right aperture given the distance and desired depth of field.

There are a number of online depth of field calculators available (search for it, since these answers live a long time I hesitate to put specific links). Put in your focal length, distance, sensor information as appropriate (ones that do not ask about sensor will be less accurate). You should be given a depth in front, and behind the point of focus. Adjust aperture until you get something to cover the cake. Be sure to allow for finding a way to focus on a point in the middle (and note "middle" varies, but usually is closer to the front - you can tell by the results of the calculation). If you have a specific spot to focus on instead, say that upright corner, then be sure that both front and back area of focus reach all visible areas.

Then when you shoot, bracket your shots - take one shot with a smaller and one with a larger aperture. Or maybe two or three of each progressively smaller and larger, so you can pick the best.

Secondly you can stack the deck a bit. Use the longest focal length lens you have (at least that you can fit into your studio), provided it has a decently wide aperture. Also, place any background objects as far away as you can while maintaining whatever appearance you want. Objects with less edges will look more blurred. And in post processing, you can selectively sharpen the cake while masking off the background and not sharpen it (you can of course artificially blur it in post processing as well, but you will get different opinions whether such looks natural or not).

Finally, selectively lighting the target a bit (not a lot) brighter than the background will naturally fool the eye to add a bit more emphasis, adding to the separation from depth of field.